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<p><dfn class="terminology">Theorem</dfn> Suppose that <span class="process-math">\(M, N, \frac{\partial M}{\partial y}\)</span> and <span class="process-math">\(\frac{\partial N}{\partial x}\)</span> are continuous in rectangle <span class="process-math">\(R: \alpha &lt; x &lt; \beta, \nu &lt; y&lt; \delta\text{.}\)</span> Then (<a href="" class="xref" data-knowl="./knowl/eq2_25.html" title="Equation 2.6.1">(2.6.1)</a>) is an exact ODE in <span class="process-math">\(R\)</span> (i. e., there exists a <span class="process-math">\(\Psi(x, y)\)</span> such that (<a href="" class="xref" data-knowl="./knowl/eq2_26.html" title="Equation 2.6.2">(2.6.2)</a>) is satisfied) if and only if</p>
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\begin{equation}
\frac{\partial N}{\partial x}=\frac{\partial M}{\partial y} \quad \textrm{in}~ R\tag{2.6.3}
\end{equation}
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